Question

We have accepted from the trilogy and from the site that the Rabbi’s view is that you cannot really “learn” aggadah or the Hebrew Bible (Tanakh) in the sense of deriving instructions or ideas from them that were not already with us beforehand.
That is in contrast to Jewish law, which has an objective content-structure, and whose texts do in fact contain normative claims that can change things for us (that is, we would be obligated to accept them as “what the text says” even if it does not fit with everything else for us).
I’ll give an example from tractate Niddah where there is a kind of “mixing of domains,” from tractate Niddah 45:
In the Mishnah it says that a girl’s vows are examined from age 11, and a boy’s from age 12.
And in the Talmud, that is Rabbi’s opinion, but Rabbi Shimon ben Elazar disagrees and holds the reverse—that a boy from age 11 and a girl from age 12.
The Talmud asks: “What is Rabbi’s reason? For it is written, ‘And the Lord God built the rib’—this teaches that extra understanding was given to a woman more than to a man. And the other one needs it for the teaching of Reish Lakish, for Reish Lakish said… ‘And the Lord God built the rib’… this teaches that the Holy One, blessed be He, braided Eve’s hair and brought her to the first man, for in the coastal cities they call braiding ‘building’.”
Here we see that the “give-and-take” that each side must provide in a halakhic discussion (which, if I understood your words correctly, is one of the pillars that make halakhic discussion more “real” than discussion of the Hebrew Bible or aggadah) can also be given in a completely aggadic way, interpreting the verse as making a factual claim and not a normative one.
There are other cases like this passage as well (where, in the ping-pong of “how each one expounds,” someone shifts into an aggadic exposition), and seemingly this shows that the Sages also viewed aggadah as serious learning.
I would add that there are often quasi-halakhic discussions about aggadic matters too (for example, the long discussion in tractate Sanhedrin about whether redemption depends on repentance, or the discussion in tractate Rosh Hashanah about when the world was created).
Could our Rabbi sharpen the point for us on this issue—is there really such a sharp boundary line between the fields? And perhaps the reason aggadah is so elusive is simply conceptual ambiguity (it is less clear what exactly is being discussed than in “an ox,” “virginity,” or “the rose-like membrane”), but with the proper depth of analysis (or at least if we had all the interpretive tools of the Sages) it would indeed be possible to learn substantive content from it?